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- Derivada de:
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Derivada de (t^(2)+1)÷(t^(1÷2)-1)
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Expresiones idénticas
- (x*log(uno + uno /x))^(x^ cinco)
- (x multiplicar por logaritmo de (1 más 1 dividir por x)) en el grado (x en el grado 5)
- (x multiplicar por logaritmo de (uno más uno dividir por x)) en el grado (x en el grado cinco)
- (x*log(1+1/x))(x5)
- x*log1+1/xx5
- (x*log(1+1/x))^(x⁵)
- (xlog(1+1/x))^(x^5)
- (xlog(1+1/x))(x5)
- xlog1+1/xx5
- xlog1+1/x^x^5
- (x*log(1+1 dividir por x))^(x^5)
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Expresiones semejantes
- (x*log(1-1/x))^(x^5)
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Expresiones con funciones
- Logaritmo log
- log(x+4)^2+2*x+7
- log(x+14)^11-11*x+7
- log(x^2)^(3)
- log(x+1)/x^2
- log(2x)
Derivada de (x*log(1+1/x))^(x^5)
Solución
Ha introducido
[src]
/ 5\
\x /
/ / 1\\
|x*log|1 + -||
\ \ x//
$$\left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}}$$
(x*log(1 + 1/x))^(x^5)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ 4 / 1 / 1\\\
| x *|- --------- + log|1 + -|||
/ 5\ | | / 1\ \ x/||
\x / | | x*|1 + -| ||
/ / 1\\ | 4 / / 1\\ \ \ x/ /|
|x*log|1 + -|| *|5*x *log|x*log|1 + -|| + -----------------------------|
\ \ x// | \ \ x// / 1\ |
| log|1 + -| |
\ \ x/ /
$$\left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} \left(\frac{x^{4} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 5 x^{4} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right)$$
Segunda derivada
[src]
/ 2 \
| / 1 / 1\\ 2 / 1 / 1\\ / 1 / 1\\|
| | - --------- + log|1 + -|| 9*x *|- --------- + log|1 + -|| x*|- --------- + log|1 + -|||
/ 5\ | | / 1\ \ x/| | / 1\ \ x/| | / 1\ \ x/||
\x / | | x*|1 + -| | | x*|1 + -| | | x*|1 + -| ||
/ / 1\\ | 7 | / / 1\\ \ x/ | 1 2 / / 1\\ \ \ x/ / \ \ x/ /|
x*|x*log|1 + -|| *|x *|5*log|x*log|1 + -|| + ------------------------| - ------------------- + 20*x *log|x*log|1 + -|| + ------------------------------- + ----------------------------|
\ \ x// | | \ \ x// / 1\ | 2 \ \ x// / 1\ / 1\ 2/ 1\ |
| | log|1 + -| | / 1\ / 1\ log|1 + -| |1 + -|*log |1 + -| |
| \ \ x/ / |1 + -| *log|1 + -| \ x/ \ x/ \ x/ |
\ \ x/ \ x/ /
$$x \left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} \left(x^{7} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right)^{2} + \frac{9 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 20 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} - \frac{1}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}}\right)$$
3-я производная
[src]
/ 3 \
| / 1 / 1\\ 1 / 1\ / 1 / 1\\ / 1 / 1\\ / 2 / 1 / 1\\ / 1 / 1\\\ 2 / 1 / 1\\ / 1 / 1\\|
| | - --------- + log|1 + -|| - --------- + log|1 + -| 2*|- --------- + log|1 + -|| | - --------- + log|1 + -|| | 9*x *|- --------- + log|1 + -|| x*|- --------- + log|1 + -||| 47*x *|- --------- + log|1 + -|| 11*x*|- --------- + log|1 + -|||
/ 5\ | | / 1\ \ x/| / 1\ \ x/ | / 1\ \ x/| | / 1\ \ x/| | | / 1\ \ x/| | / 1\ \ x/|| | / 1\ \ x/| | / 1\ \ x/||
\x / | | x*|1 + -| | x*|1 + -| | x*|1 + -| | | x*|1 + -| | | | x*|1 + -| | | x*|1 + -| || | x*|1 + -| | | x*|1 + -| ||
/ / 1\\ | 12 | / / 1\\ \ x/ | 10 2 / / 1\\ \ x/ 2 2 \ \ x/ / 5 | / / 1\\ \ x/ | | 1 2 / / 1\\ \ \ x/ / \ \ x/ /| \ \ x/ / \ \ x/ /|
|x*log|1 + -|| *|x *|5*log|x*log|1 + -|| + ------------------------| - ------------------- + 60*x *log|x*log|1 + -|| + ------------------------ - --------------------- - ---------------------- + ---------------------------- + 3*x *|5*log|x*log|1 + -|| + ------------------------|*|- ------------------- + 20*x *log|x*log|1 + -|| + ------------------------------- + ----------------------------| + -------------------------------- + -------------------------------|
\ \ x// | | \ \ x// / 1\ | 2 \ \ x// 2 3 3 2 | \ \ x// / 1\ | | 2 \ \ x// / 1\ / 1\ 2/ 1\ | / 1\ / 1\ 2/ 1\ |
| | log|1 + -| | / 1\ / 1\ / 1\ 2/ 1\ / 1\ / 1\ / 1\ 2/ 1\ / 1\ 3/ 1\ | log|1 + -| | | / 1\ / 1\ log|1 + -| |1 + -|*log |1 + -| | log|1 + -| |1 + -|*log |1 + -| |
| \ \ x/ / |1 + -| *log|1 + -| |1 + -| *log |1 + -| x*|1 + -| *log|1 + -| x*|1 + -| *log |1 + -| |1 + -| *log |1 + -| \ \ x/ / | |1 + -| *log|1 + -| \ x/ \ x/ \ x/ | \ x/ \ x/ \ x/ |
\ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ \ x/ \ x/ / /
$$\left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} \left(x^{12} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right)^{3} + 3 x^{5} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right) \left(\frac{9 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 20 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} - \frac{1}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}}\right) + \frac{47 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 60 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{11 x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} + \frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}^{2}} + \frac{2 \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}^{3}} - \frac{10}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}} - \frac{2}{x \left(1 + \frac{1}{x}\right)^{3} \log{\left(1 + \frac{1}{x} \right)}} - \frac{2}{x \left(1 + \frac{1}{x}\right)^{3} \log{\left(1 + \frac{1}{x} \right)}^{2}}\right)$$
Tercera derivada
[src]
/ 3 \
| / 1 / 1\\ 1 / 1\ / 1 / 1\\ / 1 / 1\\ / 2 / 1 / 1\\ / 1 / 1\\\ 2 / 1 / 1\\ / 1 / 1\\|
| | - --------- + log|1 + -|| - --------- + log|1 + -| 2*|- --------- + log|1 + -|| | - --------- + log|1 + -|| | 9*x *|- --------- + log|1 + -|| x*|- --------- + log|1 + -||| 47*x *|- --------- + log|1 + -|| 11*x*|- --------- + log|1 + -|||
/ 5\ | | / 1\ \ x/| / 1\ \ x/ | / 1\ \ x/| | / 1\ \ x/| | | / 1\ \ x/| | / 1\ \ x/|| | / 1\ \ x/| | / 1\ \ x/||
\x / | | x*|1 + -| | x*|1 + -| | x*|1 + -| | | x*|1 + -| | | | x*|1 + -| | | x*|1 + -| || | x*|1 + -| | | x*|1 + -| ||
/ / 1\\ | 12 | / / 1\\ \ x/ | 10 2 / / 1\\ \ x/ 2 2 \ \ x/ / 5 | / / 1\\ \ x/ | | 1 2 / / 1\\ \ \ x/ / \ \ x/ /| \ \ x/ / \ \ x/ /|
|x*log|1 + -|| *|x *|5*log|x*log|1 + -|| + ------------------------| - ------------------- + 60*x *log|x*log|1 + -|| + ------------------------ - --------------------- - ---------------------- + ---------------------------- + 3*x *|5*log|x*log|1 + -|| + ------------------------|*|- ------------------- + 20*x *log|x*log|1 + -|| + ------------------------------- + ----------------------------| + -------------------------------- + -------------------------------|
\ \ x// | | \ \ x// / 1\ | 2 \ \ x// 2 3 3 2 | \ \ x// / 1\ | | 2 \ \ x// / 1\ / 1\ 2/ 1\ | / 1\ / 1\ 2/ 1\ |
| | log|1 + -| | / 1\ / 1\ / 1\ 2/ 1\ / 1\ / 1\ / 1\ 2/ 1\ / 1\ 3/ 1\ | log|1 + -| | | / 1\ / 1\ log|1 + -| |1 + -|*log |1 + -| | log|1 + -| |1 + -|*log |1 + -| |
| \ \ x/ / |1 + -| *log|1 + -| |1 + -| *log |1 + -| x*|1 + -| *log|1 + -| x*|1 + -| *log |1 + -| |1 + -| *log |1 + -| \ \ x/ / | |1 + -| *log|1 + -| \ x/ \ x/ \ x/ | \ x/ \ x/ \ x/ |
\ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ \ \ x/ \ x/ / /
$$\left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} \left(x^{12} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right)^{3} + 3 x^{5} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right) \left(\frac{9 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 20 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} - \frac{1}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}}\right) + \frac{47 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 60 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{11 x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} + \frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}^{2}} + \frac{2 \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}^{3}} - \frac{10}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}} - \frac{2}{x \left(1 + \frac{1}{x}\right)^{3} \log{\left(1 + \frac{1}{x} \right)}} - \frac{2}{x \left(1 + \frac{1}{x}\right)^{3} \log{\left(1 + \frac{1}{x} \right)}^{2}}\right)$$
Gráfico